Question

line segment AB has endpoints A (7.5,4.2) and B (2.3,5.4). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3

Answer 1

9514 1404 393

Answer:

(6.2, 4.5)

Explanation:

We want, for some point P, ...

(P -A) / (B -P) = 1 / 3

3(P -A) = (B - P) . . . . . multiply by 3

4P = B +3A . . . . . . . . add P+3A

P = (B +3A)/4 . . . . . . .divide by 4

Filling in the coordinate values, we can find P to be ...

P = ((2.3, 5.4) +3(7.5, 4.2))/4 = (2.3+22.5, 5.4+12.6)/4

P = (6.2, 4.5)